{
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   "metadata": {},
   "source": [
    "Back to the main [Index](../index.ipynb) <a id=\"top\"></a>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Phonons and Born effective charges with Abinit and AbiPy"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This lesson discusses how to compute phonon band structures, DOS \n",
    "and Born effective charges with Abinit and AbiPy.\n",
    "The discussion closely follows the [second lesson](https://docs.abinit.org/tutorial/rf2/index.html)\n",
    "on DFPT available on the Abinit web site. \n",
    "More specifically, we will discuss how to\n",
    "\n",
    "   * Perform a convergence study for the phonon frequencies at $\\Gamma$ as function of `ecut`\n",
    "   * Compute the full phonon band structure of `AlAs` with the inclusion of LO-TO splitting\n",
    "   * Obtain thermodynamic properties within the harmonic approximation\n",
    "\n",
    "We assume that you have read the references mentioned in the [first Abinit lesson](https://docs.abinit.org/tutorial/rf1/index.html)\n",
    "on DFPT.\n",
    "You might find additional material, related to the present section, in the following references: \n",
    "   \n",
    "* [Dynamical matrices, Born effective charges, dielectric permittivity tensors, and interatomic force constants from density-functional perturbation theory](https://journals.aps.org/prb/abstract/10.1103/PhysRevB.55.10355)\n",
    "* [Phonons and related crystal properties from density-functional perturbation theory](https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.73.515)\n",
    "\n",
    "If you are already familiar with python and AbiPy-Abinit are already installed and configured,\n",
    "you may want to use directly the command line interface.\n",
    "See the README.md file in the directory of this lesson explaining how to analyze the data from the shell\n",
    "using ipython and matplotlib.\n",
    "\n",
    "## Table of Contents\n",
    "[[back to top](#top)]\n",
    "\n",
    "- [Phonon frequencies at $\\Gamma$ as function of ecut](#Phonon-frequencies-at-$\\Gamma$-as-function-of-ecut)\n",
    "- [Convergence study at $\\Gamma$](#Convergence-study-at-$\\Gamma$)\n",
    "- [Phonon band structure of AlAs](#Phonon-band-structure-of-AlAs)\n",
    "- [Post-processing the results](#Post-processing-the-results)\n",
    "- [Macroscopic dielectric tensor and Born effective-charges](#Macroscopic-dielectric-tensor-and-Born-effective-charges)\n",
    "- [Thermodynamic properties within the harmonic approximation](#Thermodynamic-properties-within-the-harmonic-approximation)\n",
    "- [Exercises](#Exercises)"
   ]
  },
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   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Phonon frequencies at $\\Gamma$ as function of ecut\n",
    "[[back to top](#top)]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Before starting, we need to import the python modules and the functions we will need in the notebook:"
   ]
  },
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   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
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    "# Use this at the beginning of your script so that your code will be compatible with python3\n",
    "from __future__ import print_function, division, unicode_literals\n",
    "\n",
    "import numpy as np\n",
    "import warnings\n",
    "warnings.filterwarnings(\"ignore\") # to get rid of deprecation warnings\n",
    "\n",
    "from abipy import abilab\n",
    "abilab.enable_notebook() # This line tells AbiPy we are running inside a notebook\n",
    "import abipy.flowtk as flowtk\n",
    "\n",
    "# This line configures matplotlib to show figures embedded in the notebook.\n",
    "# Replace `inline` with `notebook` in classic notebook\n",
    "%matplotlib inline   \n",
    "\n",
    "# Option available in jupyterlab. See https://github.com/matplotlib/jupyter-matplotlib\n",
    "#%matplotlib widget "
   ]
  },
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   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "and an useful function from the `lesson_dfpt` module that will be used to generate our DFPT flows:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
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       "<h2></h2>\n",
       "\n",
       "<div class=\"highlight\"><pre><span></span><span class=\"k\">def</span> <span class=\"nf\">make_scf_input</span><span class=\"p\">(</span><span class=\"n\">ecut</span><span class=\"o\">=</span><span class=\"mi\">2</span><span class=\"p\">,</span> <span class=\"n\">ngkpt</span><span class=\"o\">=</span><span class=\"p\">(</span><span class=\"mi\">4</span><span class=\"p\">,</span> <span class=\"mi\">4</span><span class=\"p\">,</span> <span class=\"mi\">4</span><span class=\"p\">)):</span>\n",
       "    <span class=\"sd\">&quot;&quot;&quot;</span>\n",
       "<span class=\"sd\">    This function constructs an `AbinitInput` to perform a GS-SCF calculation in crystalline AlAs.</span>\n",
       "\n",
       "<span class=\"sd\">    Args:</span>\n",
       "<span class=\"sd\">        ecut: cutoff energy in Ha.</span>\n",
       "<span class=\"sd\">        ngkpt: 3 integers specifying the k-mesh for the electrons.</span>\n",
       "\n",
       "<span class=\"sd\">    Return:</span>\n",
       "<span class=\"sd\">        `AbinitInput` object</span>\n",
       "<span class=\"sd\">    &quot;&quot;&quot;</span>\n",
       "    <span class=\"c1\"># Initialize the AlAs structure from an internal database. Use the pseudos shipped with AbiPy.</span>\n",
       "    <span class=\"n\">gs_inp</span> <span class=\"o\">=</span> <span class=\"n\">abilab</span><span class=\"o\">.</span><span class=\"n\">AbinitInput</span><span class=\"p\">(</span><span class=\"n\">structure</span><span class=\"o\">=</span><span class=\"n\">abidata</span><span class=\"o\">.</span><span class=\"n\">structure_from_ucell</span><span class=\"p\">(</span><span class=\"s2\">&quot;AlAs&quot;</span><span class=\"p\">),</span>\n",
       "                                <span class=\"n\">pseudos</span><span class=\"o\">=</span><span class=\"n\">abidata</span><span class=\"o\">.</span><span class=\"n\">pseudos</span><span class=\"p\">(</span><span class=\"s2\">&quot;13al.981214.fhi&quot;</span><span class=\"p\">,</span> <span class=\"s2\">&quot;33as.pspnc&quot;</span><span class=\"p\">))</span>\n",
       "\n",
       "    <span class=\"c1\"># Set the value of the Abinit variables needed for GS runs.</span>\n",
       "    <span class=\"n\">gs_inp</span><span class=\"o\">.</span><span class=\"n\">set_vars</span><span class=\"p\">(</span>\n",
       "        <span class=\"n\">nband</span><span class=\"o\">=</span><span class=\"mi\">4</span><span class=\"p\">,</span>\n",
       "        <span class=\"n\">ecut</span><span class=\"o\">=</span><span class=\"n\">ecut</span><span class=\"p\">,</span>\n",
       "        <span class=\"n\">ngkpt</span><span class=\"o\">=</span><span class=\"n\">ngkpt</span><span class=\"p\">,</span>\n",
       "        <span class=\"n\">nshiftk</span><span class=\"o\">=</span><span class=\"mi\">4</span><span class=\"p\">,</span>\n",
       "        <span class=\"n\">shiftk</span><span class=\"o\">=</span><span class=\"p\">[</span><span class=\"mf\">0.0</span><span class=\"p\">,</span> <span class=\"mf\">0.0</span><span class=\"p\">,</span> <span class=\"mf\">0.5</span><span class=\"p\">,</span>   <span class=\"c1\"># This gives the usual fcc Monkhorst-Pack grid</span>\n",
       "                <span class=\"mf\">0.0</span><span class=\"p\">,</span> <span class=\"mf\">0.5</span><span class=\"p\">,</span> <span class=\"mf\">0.0</span><span class=\"p\">,</span>\n",
       "                <span class=\"mf\">0.5</span><span class=\"p\">,</span> <span class=\"mf\">0.0</span><span class=\"p\">,</span> <span class=\"mf\">0.0</span><span class=\"p\">,</span>\n",
       "                <span class=\"mf\">0.5</span><span class=\"p\">,</span> <span class=\"mf\">0.5</span><span class=\"p\">,</span> <span class=\"mf\">0.5</span><span class=\"p\">],</span>\n",
       "        <span class=\"n\">ixc</span><span class=\"o\">=</span><span class=\"mi\">1</span><span class=\"p\">,</span>\n",
       "        <span class=\"n\">nstep</span><span class=\"o\">=</span><span class=\"mi\">25</span><span class=\"p\">,</span>\n",
       "        <span class=\"n\">diemac</span><span class=\"o\">=</span><span class=\"mf\">9.0</span><span class=\"p\">,</span>\n",
       "        <span class=\"n\">tolvrs</span><span class=\"o\">=</span><span class=\"mf\">1.0e-10</span><span class=\"p\">,</span>\n",
       "        <span class=\"c1\">#iomode=3,</span>\n",
       "    <span class=\"p\">)</span>\n",
       "\n",
       "    <span class=\"k\">return</span> <span class=\"n\">gs_inp</span>\n",
       "</pre></div>\n",
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     },
     "execution_count": 2,
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   ],
   "source": [
    "from lesson_dfpt import make_scf_input\n",
    "abilab.print_source(make_scf_input)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The function makes some assumptions for important parameters such as \n",
    "the crystalline structure and the pseudos. \n",
    "This is done on purpose to keep the code as simple as possible.\n",
    "It should not be so difficult to generalize the implementation to take into account other cases.\n",
    "Let's start to play with our new function:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false,
    "scrolled": false
   },
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    {
     "data": {
      "text/html": [
       "############################################################################################<br>#                                       SECTION: basic                                      <br>############################################################################################<br> <a href=\"https://docs.abinit.org/variables/basic#nband\" target=\"_blank\">nband</a> 4<br> <a href=\"https://docs.abinit.org/variables/basic#ecut\" target=\"_blank\">ecut</a> 2<br> <a href=\"https://docs.abinit.org/variables/basic#ngkpt\" target=\"_blank\">ngkpt</a> 4 4 4<br> <a href=\"https://docs.abinit.org/variables/basic#nshiftk\" target=\"_blank\">nshiftk</a> 4<br> <a href=\"https://docs.abinit.org/variables/basic#shiftk\" target=\"_blank\">shiftk</a><br>    0.0    0.0    0.5<br>    0.0    0.5    0.0<br>    0.5    0.0    0.0<br>    0.5    0.5    0.5<br> <a href=\"https://docs.abinit.org/variables/basic#ixc\" target=\"_blank\">ixc</a> 1<br> <a href=\"https://docs.abinit.org/variables/basic#nstep\" target=\"_blank\">nstep</a> 25<br> <a href=\"https://docs.abinit.org/variables/basic#tolvrs\" target=\"_blank\">tolvrs</a> 1e-10<br>############################################################################################<br>#                                      SECTION: gstate                                      <br>############################################################################################<br> <a href=\"https://docs.abinit.org/variables/gstate#diemac\" target=\"_blank\">diemac</a> 9.0<br>############################################################################################<br>#                                         STRUCTURE                                         <br>############################################################################################<br> <a href=\"https://docs.abinit.org/variables/basic#natom\" target=\"_blank\">natom</a> 2<br> <a href=\"https://docs.abinit.org/variables/basic#ntypat\" target=\"_blank\">ntypat</a> 2<br> <a href=\"https://docs.abinit.org/variables/basic#typat\" target=\"_blank\">typat</a> 1 2<br> <a href=\"https://docs.abinit.org/variables/basic#znucl\" target=\"_blank\">znucl</a> 13 33<br> <a href=\"https://docs.abinit.org/variables/basic#xred\" target=\"_blank\">xred</a><br>    0.0000000000    0.0000000000    0.0000000000<br>    0.2500000000    0.2500000000    0.2500000000<br> <a href=\"https://docs.abinit.org/variables/basic#acell\" target=\"_blank\">acell</a>    1.0    1.0    1.0<br> <a href=\"https://docs.abinit.org/variables/basic#rprim\" target=\"_blank\">rprim</a><br>    0.0000000000    5.3050000000    5.3050000000<br>    5.3050000000    0.0000000000    5.3050000000<br>    5.3050000000    5.3050000000    0.0000000000"
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       "<AbinitInput at 26266033680>"
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   ],
   "source": [
    "scf_input = make_scf_input()\n",
    "scf_input"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Full Formula (Al1 As1)\n",
      "Reduced Formula: AlAs\n",
      "abc   :   3.970101   3.970101   3.970101\n",
      "angles:  60.000000  60.000000  60.000000\n",
      "Sites (2)\n",
      "  #  SP       a     b     c\n",
      "---  ----  ----  ----  ----\n",
      "  0  Al    0     0     0\n",
      "  1  As    0.25  0.25  0.25\n"
     ]
    }
   ],
   "source": [
    "print(scf_input.structure)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "scf_input.structure.plot();"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We are using the same pseudopotentials than the official tutorial.\n",
    "Note that the xc functional is LDA in both pseudos but with a different\n",
    "parametrization. This is the reason why we are using `ixc` in the input file."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "<NcAbinitPseudo: 13al.981214.fhi>\n",
      "  summary: Aluminum, fhi98PP : Hamann-type, LDA CA PerdewWang, l=2 local\n",
      "  number of valence electrons: 3.0\n",
      "  maximum angular momentum: d\n",
      "  angular momentum for local part: d\n",
      "  XC correlation: PW\n",
      "  supports spin-orbit: False\n",
      "  radius for non-linear core correction: 0.0\n",
      "  hint for low accuracy: ecut: 0.0, pawecutdg: 0.0\n",
      "  hint for normal accuracy: ecut: 0.0, pawecutdg: 0.0\n",
      "  hint for high accuracy: ecut: 0.0, pawecutdg: 0.0 \n",
      "\n",
      "<NcAbinitPseudo: 33as.pspnc>\n",
      "  summary: Troullier-Martins psp for element  As        Thu Oct 27 17:37:14 EDT 1994\n",
      "  number of valence electrons: 5.0\n",
      "  maximum angular momentum: p\n",
      "  angular momentum for local part: p\n",
      "  XC correlation: LDA_XC_TETER93\n",
      "  supports spin-orbit: False\n",
      "  radius for non-linear core correction: 2.0573171556401\n",
      "  hint for low accuracy: ecut: 0.0, pawecutdg: 0.0\n",
      "  hint for normal accuracy: ecut: 0.0, pawecutdg: 0.0\n",
      "  hint for high accuracy: ecut: 0.0, pawecutdg: 0.0 \n",
      "\n"
     ]
    }
   ],
   "source": [
    "for pseudo in scf_input.pseudos:\n",
    "    print(pseudo, \"\\n\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "As you can see, we essentialy have a standard input to perform a GS calculation. This object will represent\n",
    "the **building block** for our DFPT calculation with AbiPy.\n",
    "\n",
    "It this is not your first time you use the DFPT part of Abinit, you already know that phonon calculations\n",
    "require an initial GS run to produce the `WFK` file \n",
    "followed by a DFPT run that reads the `WFK` file and solves the Sternheimer equations for $N_{\\text{irred}}(q)$ \n",
    "atomic perturbations where $N_{\\text{irred}}$ is the number of independent atomic displacements (assuming $q$ belongs to the k-mesh).\n",
    "\n",
    "If you try to do a convergence study wrt `ecut` **without multi-datasets**, you will likely start from an initial GS input file with a given value of `ecut`, use it as a template to generate the DFPT input files, create symbolic \n",
    "links to the `WFK` file produced in the first GS step and then instruct Abinit to read this file with `irdwfk`.\n",
    "Once you have a set of input files that work for a particular `ecut`, one can simply replicate the set of \n",
    "directories and files and use a script to change the value of `ecut` in the input files.\n",
    "Then, of course, one has to run the calculations manually, collect the results and produce nice plots to understand\n",
    "what is happening.\n",
    "\n",
    "This approach is obviously boring and error-prone if you are a human being but it is easy to implement in an algorithm \n",
    "and machines do not complain if they have a lot of repetive work to do!\n",
    "There are also several **technical advantages** in using this **task-based approach vs multi-datasets** but we discuss this point in more details afterwards. \n",
    "\n",
    "If the machine could speak, it will tell you: give me an object that represents an input for GS calculations,\n",
    "give me the list of q-points you want to compute as well as the parameters that must be changed in the initial input \n",
    "and I will generate a `Flow` for DFPT calculations.\n",
    "This logic appears so frequenty that we decided to encapsulate it in the `flowtk.phonon_conv_flow` factory function: "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
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       "<h2></h2>\n",
       "\n",
       "<div class=\"highlight\"><pre><span></span><span class=\"k\">def</span> <span class=\"nf\">build_flow_alas_ecut_conv</span><span class=\"p\">(</span><span class=\"n\">options</span><span class=\"p\">):</span>\n",
       "    <span class=\"sd\">&quot;&quot;&quot;</span>\n",
       "<span class=\"sd\">    Build and return Flow for convergence study of phonon frequencies at Gamma as function of ecut.</span>\n",
       "<span class=\"sd\">    &quot;&quot;&quot;</span>\n",
       "    <span class=\"n\">scf_input</span> <span class=\"o\">=</span> <span class=\"n\">make_scf_input</span><span class=\"p\">()</span>\n",
       "    <span class=\"k\">return</span> <span class=\"n\">flowtk</span><span class=\"o\">.</span><span class=\"n\">phonon_conv_flow</span><span class=\"p\">(</span><span class=\"s2\">&quot;flow_alas_ecut_conv&quot;</span><span class=\"p\">,</span> <span class=\"n\">scf_input</span><span class=\"p\">,</span> <span class=\"n\">qpoints</span><span class=\"o\">=</span><span class=\"p\">(</span><span class=\"mi\">0</span><span class=\"p\">,</span> <span class=\"mi\">0</span><span class=\"p\">,</span> <span class=\"mi\">0</span><span class=\"p\">),</span>\n",
       "                                   <span class=\"n\">params</span><span class=\"o\">=</span><span class=\"p\">[</span><span class=\"s2\">&quot;ecut&quot;</span><span class=\"p\">,</span> <span class=\"p\">[</span><span class=\"mi\">4</span><span class=\"p\">,</span> <span class=\"mi\">6</span><span class=\"p\">,</span> <span class=\"mi\">8</span><span class=\"p\">]])</span>\n",
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     },
     "execution_count": 7,
     "metadata": {},
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    }
   ],
   "source": [
    "from lesson_dfpt import build_flow_alas_ecut_conv\n",
    "abilab.print_source(build_flow_alas_ecut_conv)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's call the function to build our flow:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "<Flow, node_id=345794, workdir=flow_alas_ecut_conv>\n",
      "Number of works: 6, total number of tasks: 9\n",
      "Number of tasks with a given class:\n",
      "\n",
      "Task Class      Number\n",
      "------------  --------\n",
      "ScfTask              3\n",
      "PhononTask           6"
     ]
    }
   ],
   "source": [
    "flow = build_flow_alas_ecut_conv(options=None)\n",
    "\n",
    "flow.show_info()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "and call the `get_graphviz` method to visualize the connection among the `Tasks`:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
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       "<text text-anchor=\"middle\" x=\"310.042\" y=\"-199.471\" font-family=\"Times,serif\" font-size=\"8.00\">PhononTask</text>\n",
       "</g>\n",
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       "</g>\n",
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       "<text text-anchor=\"middle\" x=\"272.024\" y=\"-55.3282\" font-family=\"Times,serif\" font-size=\"8.00\">ScfTask</text>\n",
       "</g>\n",
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       "</g>\n",
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       "</g>\n",
       "</g>\n",
       "</svg>\n"
      ],
      "text/plain": [
       "<graphviz.dot.Digraph at 0x1a2ab95908>"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "flow.get_graphviz()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# matplotlib version based on networkx\n",
    "#flow.plot_networkx(with_edge_labels=True);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The flow contains three independent groups of tasks, one group per each value of `ecut` specified in `params`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "w0_t0 uses ecut: 4\n",
      "w1_t0 uses ecut: 4\n",
      "w1_t1 uses ecut: 4\n",
      "w2_t0 uses ecut: 6\n",
      "w3_t0 uses ecut: 6\n",
      "w3_t1 uses ecut: 6\n",
      "w4_t0 uses ecut: 8\n",
      "w5_t0 uses ecut: 8\n",
      "w5_t1 uses ecut: 8\n"
     ]
    }
   ],
   "source": [
    "for work in flow:\n",
    "    for task in work:\n",
    "        print(task.pos_str, \"uses ecut:\", task.input[\"ecut\"])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
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       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>ecut</th>\n",
       "      <th>class</th>\n",
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       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>w0_t0</th>\n",
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       "    <tr>\n",
       "      <th>w1_t0</th>\n",
       "      <td>4</td>\n",
       "      <td>PhononTask</td>\n",
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       "      <th>w1_t1</th>\n",
       "      <td>4</td>\n",
       "      <td>PhononTask</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>w2_t0</th>\n",
       "      <td>6</td>\n",
       "      <td>ScfTask</td>\n",
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       "      <td>8</td>\n",
       "      <td>ScfTask</td>\n",
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       "    <tr>\n",
       "      <th>w5_t0</th>\n",
       "      <td>8</td>\n",
       "      <td>PhononTask</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>w5_t1</th>\n",
       "      <td>8</td>\n",
       "      <td>PhononTask</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "       ecut       class\n",
       "w0_t0     4     ScfTask\n",
       "w1_t0     4  PhononTask\n",
       "w1_t1     4  PhononTask\n",
       "w2_t0     6     ScfTask\n",
       "w3_t0     6  PhononTask\n",
       "w3_t1     6  PhononTask\n",
       "w4_t0     8     ScfTask\n",
       "w5_t0     8  PhononTask\n",
       "w5_t1     8  PhononTask"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "flow.get_vars_dataframe(\"ecut\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Each group represents a `Workflow` and consists of one `ScfTask`(red circle) that solves the `KS` equations self-consistently producing a `WFK` file that will be used by the two children (`PhononTasks` - blue circles)\n",
    "to compute the first-order change of the wavefunctions due to one of the *irreducible* atomic pertubations.\n",
    "\n",
    "Note that `phonon_conv_flow` invokes Abinit under the hood to get the list of irreducible perturbations \n",
    "and uses this information to build the flow.\n",
    "This explains why we have two `PhononTasks` per $q$-point instead of the total number of phonon modes that \n",
    "equals $3*N_{atom}=6$.\n",
    "\n",
    "Perhaps a table with the values of the input variables associated to the DFPT perturbation will help.\n",
    "`None` means that the variable is not defined in that particular input."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
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       "  <thead>\n",
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       "      <th></th>\n",
       "      <th>rfphon</th>\n",
       "      <th>rfatpol</th>\n",
       "      <th>rfdir</th>\n",
       "      <th>qpt</th>\n",
       "      <th>kptopt</th>\n",
       "      <th>class</th>\n",
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       "      <td>2</td>\n",
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       "      <td>2</td>\n",
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       "    </tr>\n",
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       "</table>\n",
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      ],
      "text/plain": [
       "      rfphon rfatpol      rfdir              qpt kptopt       class\n",
       "w0_t0   None    None       None             None   None     ScfTask\n",
       "w1_t0      1  [1, 1]  [1, 0, 0]  [0.0, 0.0, 0.0]      2  PhononTask\n",
       "w1_t1      1  [2, 2]  [1, 0, 0]  [0.0, 0.0, 0.0]      2  PhononTask\n",
       "w2_t0   None    None       None             None   None     ScfTask\n",
       "w3_t0      1  [1, 1]  [1, 0, 0]  [0.0, 0.0, 0.0]      2  PhononTask\n",
       "w3_t1      1  [2, 2]  [1, 0, 0]  [0.0, 0.0, 0.0]      2  PhononTask\n",
       "w4_t0   None    None       None             None   None     ScfTask\n",
       "w5_t0      1  [1, 1]  [1, 0, 0]  [0.0, 0.0, 0.0]      2  PhononTask\n",
       "w5_t1      1  [2, 2]  [1, 0, 0]  [0.0, 0.0, 0.0]      2  PhononTask"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "flow.get_vars_dataframe(\"rfphon\", \"rfatpol\", \"rfdir\", \"qpt\", \"kptopt\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "If the meaning of these variables is not clear, you can consult the [Abinit documentation](https://docs.abinit.org)\n",
    "e.g. [the documentation of the rfatpol input variable](https://docs.abinit.org/variables/dfpt/#rfatpol)\n",
    "or access the documentation directly from python with: "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<h2>Default value:</h2>\n",
       "<p>[1, 1]</p>\n",
       "<h2>Description:</h2>\n",
       "<p>Control the range of atoms for which displacements will be considered in\n",
       "phonon calculations (atomic polarizations), using the 2n+1 theorem.\n",
       "These values are only relevant to phonon response function calculations.\n",
       "May take values from 1 to <b>natom</b>, with <b>rfatpol</b>(1)&lt;=<b>rfatpol</b>(2).\n",
       "The atoms to be moved will be defined by the\n",
       "do-loop variable iatpol:</p>\n",
       "<ul>\n",
       "<li>do iatpol=<b>rfatpol</b>(1),<b>rfatpol</b>(2)</li>\n",
       "</ul>\n",
       "<p>For the calculation of a full dynamical matrix, use <b>rfatpol</b>(1)=1 and\n",
       "<b>rfatpol</b>(2)=<b>natom</b>, together with <b>rfdir</b> 1 1 1. For selected\n",
       "elements of the dynamical matrix, use different values of <b>rfatpol</b> and/or\n",
       "<b>rfdir</b>. The name 'iatpol' is used for the part of the internal variable\n",
       "ipert when it runs from 1 to <b>natom</b>. The internal variable ipert can also\n",
       "assume values larger than <b>natom</b>, denoting perturbations of electric field\n",
       "or stress type (see [help:respfn|the response function help file]).</p>"
      ],
      "text/plain": [
       "rfatpol  <Response Function: ATomic POLarisation>"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "abilab.docvar(\"rfatpol\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now we can generate the `flow_alas_ecut` directory with the input files by executing \n",
    "the `lesson_dfpt.py` script.\n",
    "Then use the `abirun.py` script to launch the entire calculation with:\n",
    "\n",
    "    abirun.py flow_alas_ecut_conv scheduler\n",
    "    \n",
    "You will see that all `PhononTasks` will be executed in parallel on your machine.\n",
    "\n",
    "<div class=\"alert alert-warning\">\n",
    "Please make sure that AbiPy is properly configured by running abicheck --with flow\n",
    "</div>\n",
    "\n",
    "If you prefer to skip this part, you may want to jump to the next section, that presents the post-processing of the results.\n",
    "Note that the output files are already available in the repository so it is also possible to try \n",
    "the AbiPy post-processing tools without having to run the flow."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Convergence study at $\\Gamma$\n",
    "[[back to top](#top)]\n",
    "\n",
    "There are several output files located inside the `outdata` directories:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "flow_alas_ecut_conv//w0/t0/outdata/out_DDB\n",
      "flow_alas_ecut_conv//w1/outdata/out_DDB\n",
      "flow_alas_ecut_conv//w2/t0/outdata/out_DDB\n",
      "flow_alas_ecut_conv//w3/outdata/out_DDB\n",
      "flow_alas_ecut_conv//w4/t0/outdata/out_DDB\n",
      "flow_alas_ecut_conv//w5/outdata/out_DDB\n"
     ]
    }
   ],
   "source": [
    "!find flow_alas_ecut_conv/ -name \"*_DDB\""
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Remember that our goal is to analyze the convergence of the phonon frequencies at $\\Gamma$ \n",
    "as function of `ecut`.\n",
    "So we are mainly interested in the DDB files located in the `outdata` directories \n",
    "of the `PhononWorks` (`w0/outdata`, `w1/outdata`, `w2/outdata`).\n",
    "These are indeed the DDB files with all the information needed to reconstruct the \n",
    "dynamical matrix at $\\Gamma$ and to compute the phonon frequencies (AbiPy calls `mrgddb`\n",
    "to merge the DDB files when all the perturbations in the `PhononWork` have been computed).\n",
    "\n",
    "The code below tells our robot that we would like to analyze all the DDB files \n",
    "located in the output directories of the works:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<ol start=\"0\">\n",
       "<li>flow_alas_ecut_conv/w1/outdata/out_DDB</li>\n",
       "<li>flow_alas_ecut_conv/w3/outdata/out_DDB</li>\n",
       "<li>flow_alas_ecut_conv/w5/outdata/out_DDB</li>\n",
       "</ol>"
      ],
      "text/plain": [
       "Label                                   Relpath\n",
       "--------------------------------------  --------------------------------------\n",
       "flow_alas_ecut_conv/w1/outdata/out_DDB  flow_alas_ecut_conv/w1/outdata/out_DDB\n",
       "flow_alas_ecut_conv/w3/outdata/out_DDB  flow_alas_ecut_conv/w3/outdata/out_DDB\n",
       "flow_alas_ecut_conv/w5/outdata/out_DDB  flow_alas_ecut_conv/w5/outdata/out_DDB"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "robot = abilab.DdbRobot.from_dir_glob(\"./flow_alas_ecut_conv/w*/outdata/\")\n",
    "robot"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "For more examples on the use of DDB and robots, see the \n",
    "[DDB notebook](https://nbviewer.jupyter.org/github/abinit/abitutorials/blob/master/abitutorials/ddb.ipynb).\n",
    "Now we ask the robot to call `anaddb` to compute the phonon frequencies at $\\Gamma$ for all DDBs \n",
    "and return a pandas `DataFrame`:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "data_gamma = robot.get_dataframe_at_qpoint((0, 0, 0))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The `DataFrame` is a dict-like object whose keys are the name of the colums in the table"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Index(['mode0', 'mode1', 'mode2', 'mode3', 'mode4', 'mode5', 'nkpt', 'nsppol',\n",
      "       'ecut', 'tsmear', 'occopt', 'ixc', 'nband', 'usepaw', 'formula',\n",
      "       'natom', 'alpha', 'beta', 'gamma', 'a', 'b', 'c', 'volume',\n",
      "       'abispg_num', 'spglib_symb', 'spglib_num', 'spglib_lattice_type'],\n",
      "      dtype='object')\n"
     ]
    }
   ],
   "source": [
    "print(data_gamma.keys())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "where `mode-i` is the frequency in eV of the i-th phonon mode.\n",
    "\n",
    "We are mainly interested in the convergence of the phonon frequencies versus `ecut` so we filter these columns with:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
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       "\n",
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       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>ecut</th>\n",
       "      <th>mode0</th>\n",
       "      <th>mode1</th>\n",
       "      <th>mode2</th>\n",
       "      <th>mode3</th>\n",
       "      <th>mode4</th>\n",
       "      <th>mode5</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>flow_alas_ecut_conv/w1/outdata/out_DDB</th>\n",
       "      <td>4.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.043641</td>\n",
       "      <td>0.043641</td>\n",
       "      <td>0.043641</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>flow_alas_ecut_conv/w3/outdata/out_DDB</th>\n",
       "      <td>6.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.044485</td>\n",
       "      <td>0.044485</td>\n",
       "      <td>0.044485</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>flow_alas_ecut_conv/w5/outdata/out_DDB</th>\n",
       "      <td>8.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.044625</td>\n",
       "      <td>0.044625</td>\n",
       "      <td>0.044625</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                                        ecut  mode0  mode1  mode2     mode3  \\\n",
       "flow_alas_ecut_conv/w1/outdata/out_DDB   4.0    0.0    0.0    0.0  0.043641   \n",
       "flow_alas_ecut_conv/w3/outdata/out_DDB   6.0    0.0    0.0    0.0  0.044485   \n",
       "flow_alas_ecut_conv/w5/outdata/out_DDB   8.0    0.0    0.0    0.0  0.044625   \n",
       "\n",
       "                                           mode4     mode5  \n",
       "flow_alas_ecut_conv/w1/outdata/out_DDB  0.043641  0.043641  \n",
       "flow_alas_ecut_conv/w3/outdata/out_DDB  0.044485  0.044485  \n",
       "flow_alas_ecut_conv/w5/outdata/out_DDB  0.044625  0.044625  "
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data_gamma = data_gamma[[\"ecut\"] + [k for k in data_gamma if k.startswith(\"mode\")]]\n",
    "data_gamma"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "and we get some statistics about our data with:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
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       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>ecut</th>\n",
       "      <th>mode0</th>\n",
       "      <th>mode1</th>\n",
       "      <th>mode2</th>\n",
       "      <th>mode3</th>\n",
       "      <th>mode4</th>\n",
       "      <th>mode5</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>count</th>\n",
       "      <td>3.0</td>\n",
       "      <td>3.0</td>\n",
       "      <td>3.0</td>\n",
       "      <td>3.0</td>\n",
       "      <td>3.000000</td>\n",
       "      <td>3.000000</td>\n",
       "      <td>3.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>mean</th>\n",
       "      <td>6.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.044250</td>\n",
       "      <td>0.044250</td>\n",
       "      <td>0.044250</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>std</th>\n",
       "      <td>2.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.000533</td>\n",
       "      <td>0.000533</td>\n",
       "      <td>0.000533</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>min</th>\n",
       "      <td>4.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.043641</td>\n",
       "      <td>0.043641</td>\n",
       "      <td>0.043641</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>25%</th>\n",
       "      <td>5.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.044063</td>\n",
       "      <td>0.044063</td>\n",
       "      <td>0.044063</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>50%</th>\n",
       "      <td>6.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.044485</td>\n",
       "      <td>0.044485</td>\n",
       "      <td>0.044485</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>75%</th>\n",
       "      <td>7.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.044555</td>\n",
       "      <td>0.044555</td>\n",
       "      <td>0.044555</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>max</th>\n",
       "      <td>8.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.044625</td>\n",
       "      <td>0.044625</td>\n",
       "      <td>0.044625</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "       ecut  mode0  mode1  mode2     mode3     mode4     mode5\n",
       "count   3.0    3.0    3.0    3.0  3.000000  3.000000  3.000000\n",
       "mean    6.0    0.0    0.0    0.0  0.044250  0.044250  0.044250\n",
       "std     2.0    0.0    0.0    0.0  0.000533  0.000533  0.000533\n",
       "min     4.0    0.0    0.0    0.0  0.043641  0.043641  0.043641\n",
       "25%     5.0    0.0    0.0    0.0  0.044063  0.044063  0.044063\n",
       "50%     6.0    0.0    0.0    0.0  0.044485  0.044485  0.044485\n",
       "75%     7.0    0.0    0.0    0.0  0.044555  0.044555  0.044555\n",
       "max     8.0    0.0    0.0    0.0  0.044625  0.044625  0.044625"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data_gamma.describe()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Pandas tables are extremly powerful and the `describe` method already gives some useful info \n",
    "about the convergence of the phonon modes. \n",
    "Sometimes, however, we would like to visualize the data to have a better understanding of what's happening:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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Wp8QhcgSef3cDiz/ezDnH9+PMY3OjHY5Iq1DiEGmiN5dt4akl6zhhZC8uPk1jM6TzUOIQaYKCz3fy6CJj5MAefO/c4Vo5TzoVJQ6RCK3dspf7n15Bbq8UfnThKC2UJJ1OWAMAnXOXATcB8cAsM7u3QflYYDbQDVgCXGtmNSHl44ClZpbY4LhUIB/4gZm93qBsPrDSzG6J8JpEWszWXeXcOX8ZaSmJXD85TzPaSqfU6Fcl51wf4FbgJGAscLVzbkSD3R4HppnZUCAGuCrk+GTgbiDhIKe/B/hK30Xn3PeBr4d5DSKtYk9pFTOeyCcmBqZPzaN714P9Sot0fOE8Y08AXjOzXWZWBiwALqkrdM71B5LMbGlw0yPA5JDj7wBmNTypc24qUAIsa7B9MHAl8Lewr0KkhZVX1jBzXgEl5dVcPzmPXunJ0Q5JJGrCSRy9gcKQ14VA33DKnXMTgWQzWxB6QudcP+B64OcNtscBc4BrgX3hXYJIy6qu8XPvU8vZsrOMH180ioE53aIdkkhUhVNB64P6JZDBq4ryN1bunMvGaxeZEHoy55wPLzlMM7MK51xo8S3AQjNb1WB72DIyUpp0HEBmZtucJkJxRaY54/L7A9zxj49YvWE30y89mtPHN32sRme4X81JcUWmNeMKJ3FsAk4OeZ0NbGlQnnOQ8vOADGBJXRJwzuUDVwDDgDnB7UOA2c65q/CqwKqCbRzZwWPKzOzP4V5QUVEpfn+g8R0baKuzlyquyDRnXIFAgH+9+jlL8jcz+bTBjO6f1uRzd4b71ZwUV2SOJC6fLybiL9zhJI5XgFucc5lAGXAxcHVdoZltcM5VOudONLO3ge8Ai8xsNl5PKwCccwEzGxt8mRuy/XXglmCvqmEh228Jnj/spCHSnP79/kb+8+FGJozvyzeO7xftcETajEbbOMxsM/ArYDFe19m5Zva+c+5F51zdwsmXAzOdc2uAFOCulgpYpDW8u3Ir8xZ/zrHDsvjWGUcRowF+IvXC6oRuZnOBuQ22nRvycwFwXCPnOOhfnpmddojtt4QTm0hzW7G+iIdeWM2wfmn88LwRGhUu0oCGvIqE+GJrMfc+tYKcjK5MmzSG+Dj9iYg0pL8KkaDtu8uZNa+AlC7xTJ+SR3IXjQoXORglDhGguGwfM+YVUOsPcMPUPNJTExs/SKSTUuKQTq9yXw2z5hewp6SK6ybnkZPRNdohibRpShzSqdXU+rnvqRV8ua2Uay8cxZA+3aMdkkibp8QhnVYgEOCRRWtYsX4X3/2GY+yQntEOSaRdUOKQTuvJN9bxzoqtXHjyQE7J6x3tcETaDSUO6ZRe+XAjLy7dwGnj+nD+1wZEOxyRdkWJQzqdD9Zs55+vfMa4o3ry7TOHalS4SISUOKRTWbNhNw8+t5LBfbtzzcSR+HxKGiKRUuKQTmPj9lLuXriMrPRkfnLxGBLiY6Mdkki7pMQhncLOvRXMmJdPl4Q4bpiSR0pSfLRDEmm3lDikwyutqGbmvAL2VfuZPiWPHt26RDskkXZNiUM6tKrqWu5cUMCOPZX85OLR9M1s+gqRIuJR4pAOq9bv52/PrGTd5mKumTgC1y892iGJdAhKHNIhBQIBHvv3p+R/vpPLzxrKMS4r2iGJdBhKHNIhPfPWepYUbOG8r/Xn60f3jXY4Ih2KEod0OK9/spln3/6Ck8bkcNHJg6IdjkiHo8QhHcrSFYU89rIxZnAG3z3baVS4SAvQEmfSYXy2aQ93/CufAdnd+O8LRhEXq+9FIi1Bf1nSIWzeWcZdC5aRmZ7E9ZPHkJigUeEiLUVPHNLu7SquZOa8fOJifdxy1QnE+v3RDkmkQ9MTh7Rr5ZXVzJxfQHllDddPziNby76KtDglDmm3qmtquevJ5WwtKmfapNH0z06NdkginYISh7RLfn+AB55bxacb9/DD80YwYkCPaIck0mkocUi7EwgEmPvKp3xkO/jW14dw/Ihe0Q5JpFNR4pB258WlG3jt481847h+nHVcv2iHI9LpKHFIu/LWskKefGMd/zWyF5ecPjja4Yh0Skoc0m4sW7uTRxatYeSAdL5/7nB8GhUuEhVKHNIurNtSzH1PryA3K4UfXTRao8JFokh/fdLmbd1Vzqz5BXTvmsD1U/JIStS4VZFoCusv0Dl3GXATEA/MMrN7G5SPBWYD3YAlwLVmVhNSPg5YamaJDY5LBfKBH5jZ6865WOAe4GQgBnjQzGY19eKk/dtbWsWMJ/IBuGHKWLp3TYhyRCLS6BOHc64PcCtwEjAWuNo5N6LBbo8D08xsKN4H/lUhxycDdwMH+4u/Bwhdlu17QAYwBjgu+F5Hh3010qFUVNUwc34BxeX7mD4lj149kqMdkogQXlXVBOA1M9tlZmXAAuCSukLnXH8gycyWBjc9AkwOOf4O4CtPDc65qUAJsCxk8wrgd2bmD77XOiA3/MuRjqKm1s89C5ezeUcZP75oNANzukU7JBEJCidx9AYKQ14XAn3DKXfOTQSSzWxB6Amdc/2A64Gfh243s6VmtiK4z9fwnjqWhHUl0mH4AwHmvLCa1Rt2c+U5wxg9KCPaIYlIiHDaOHxAIOR1DOBvrNw5l43XLjIh9GTOOR8wB69qq8I595U3dM6dAjwBXG5mu8OIsV5GRkokux8gM7NtznXU2eKa8+wK3lu1je+eO5wLvz404uM72/06UoorMoorvMSxCa+xuk42sKVBec5Bys/Da69YUpccnHP5wBXAMGBOcPsQYLZz7iozW+ycmwTcD0w1s9cjvaCiolL8/kDjOzaQmZnKjh0lER/X0jpbXC+99yVPv7GWM47py6mjsyN+j852v46U4opMR4zL54uJ+At3OInjFeAW51wmUAZcDFxdV2hmG5xzlc65E83sbeA7wCIzm43X0woA51zAzMYGX+aGbH8duCXYq+pYvKRxppmFtn1IJ7B05VbmLf6c8cOyuPSMo7Tsq0gb1Wgbh5ltBn4FLMbrOjvXzN53zr3onBsf3O1yYKZzbg2QAtzVxHhuwktmf3fO5Qf/m9jEc0k7svKLXcx5YTUuN42rzhuOz6ekIdJWhTWOw8zmAnMbbDs35OcCvIbsw53joJ8EZnZayM8XhBOPdCwbtpZwz8Ll5GQk8z8XjyY+Tsu+irRlGjkuUbV9TwUz5xeQ0iWO6VPGktwlPtohiUgjlDgkaorL9zHjiXxqa/1MnzKW9NTExg8SkahT4pCoqNxXw53zC9hdUsV1l+TRu6fWChdpL5Q4pNXV1Pq5/+mVfLG1hGsvGMmQvt2jHZKIRECJQ1pVIBDg0UVrWL6uiO+e7Rh3VGa0QxKRCClxSKtauGQdb6/YygUnDeTUsX2iHY6INIESh7SaVz/axAvvbuDUsb2ZeOKAaIcjIk2kxCGt4sM125n7n08Zd1RPvn3WUI0KF2nHlDikxdmXu3nguZUM7tOdayaOJNanXzuR9kx/wdKiNm0v5a4nl5OZlsRPLhlDQrxGhYu0d0oc0mKK9lYyY14+ifE+bpgylpQkjQoX6QiUOKRFlFZUM2NePlXVfm6YMpaM7l2iHZKINBMlDml2+6pruWvBMnbsqeAnF4+mb1bTF9cSkbZHiUOaVa3fz1+fWcnazXu5+vyRuH7p0Q5JRJqZEoc0m0AgwOMvf0r+5zu57MyhjB+WFe2QRKQFKHFIs3n27S94I38L3zyhP2cc0zfa4YhIC1HikGbxRv5mnnlrPSeOymbSKYOiHY6ItCAlDjlin3y2g7//2xg9KIMrzhmmUeEiHZwShxyRzzft5a/PrGRAdio/unAUcbH6lRLp6PRXLk22ZWcZdy4oID01kesm55GYoFHhIp2BEoc0SdHeCmbOyyc21scNU8fSLTkh2iGJSCuJi3YA0v6UV1bzl0c/pLSyhl9edjRZaUnRDklEWpGeOCQi1TW13P3kcjZtL2HaRaPpn50a7ZBEpJUpcUjY/P4ADz63Ctu4h+u+dTQjB/aIdkgiEgVKHBKWQCDAP1/5jA9tB1NOH8JpR2uAn0hnpcQhYXlx6QZe/XgTZx2byzeO7xftcEQkipQ4pFFvLy/kyTfWcfyIXkz5+pBohyMiUabEIYe1bG0RD7+4huH90/nBN4fj06hwkU5PiUMOaX1hMfc9vZy+mV2ZNmm0RoWLCKDEIYewbVc5s+YX0C05gelT8khK1JAfEfEocchX7C2t4o4n8gkE4IapY+mekhjtkESkDVHikANUVNUwa/4yisv3cf3kPLJ7JEc7JBFpY8Kqf3DOXQbcBMQDs8zs3gblY4HZQDdgCXCtmdWElI8DlppZYoPjUoF84Adm9npw20+Bq/CS2i/NbGHTLk0iVVPr576nlrNxeyk/uWQ0g3p3i3ZIItIGNfrE4ZzrA9wKnASMBa52zo1osNvjwDQzGwrE4H3w1x2fDNwNHGwWvHuA9JB9jwW+HXyfk4A/O+c0PLkV+AMBHnpxNSu/2M2V5wxjzOCe0Q5JRNqocKqqJgCvmdkuMysDFgCX1BU65/oDSWa2NLjpEWByyPF3ALMantQ5NxUoAZaFbD4XWGhmlWa2HXgdOC/sq5EmW7B4LUtXbmPSKYM4aUxOtMMRkTYsnKqq3kBhyOtC4LhGyvsCOOcmAslmtsA5V7+Dc64fcD3wdWBRg3N9cLBzhSsjIyWS3Q+Qmdk2J+xr6biefmMtL73/Jd88cSBXThwV9gp+nfV+NZXiioziikxrxhVO4vABgZDXMYC/sXLnXDZeu8iE0JM553zAHLyqrYrQhBLGezWqqKgUvz/Q+I4NZGamsmNHScTHtbSWjuu9VduY8+xKjnGZXHTiAHbuLG0TcTWV4oqM4opMR4zL54uJ+At3OFVVm4DQuotsYEsY5ecBGcAS51w+QPD/o4FhwJzg6/HAbOfc6WG8lzSjVV/sYvbzqxiam8bV54/A59OocBFpXDhPHK8AtzjnMoEy4GLg6rpCM9vgnKt0zp1oZm8D3wEWmdlsvJ5WADjnAmY2NvgyN2T768AtZva6c64M+JtzbgbQFTgD+M0RXaEc1JfbSrhn4XKyM5L5ycWjiY/Tsq8iEp5GnzjMbDPwK2AxXtfZuWb2vnPuRefc+OBulwMznXNrgBTgrqYEY2bv4/XQ+gB4C/h18P2lGe3YU8HMeQUkd4lj+uQ8krvERzskEWlHYgKByNsD2qgBwHq1cRxecfk+/vjYR5RWVPPLbx9Dn55d20RczUVxRUZxRaYjxhXSxjEQ+CKsY5r0TtIuVe2r5c75y9hVUsVPLhnT5KQhIp2bEkcnUVPr5/5nVvDF1mKumTiSo/qmRTskEWmnlDg6gUAgwN9fMpatLeI7ZzmOHpoZ7ZBEpB1T4ugEnnpzHW8tL2TiiQM4bVyfaIcjIu2cEkcH99rHm3j+nQ2ckpfDBScNjHY4ItIBKHF0YB/Zdv7x8qeMHdKT75ztwp5KRETkcJQ4Oij7cjd/e3YVg/p045oLRhLr0z+1iDQPfZp0QJt2lHLXk8vp2b0L112SR2K8RoWLSPNR4uhgdhVXMnNeAQnxPm6YmkdKkkaFi0jzUuLoQEorqrnjiXwq99Vww5Sx9OyeFO2QRKQDUuLoIPZV13LXk8vYsaeC/5k0htyspq9LIiJyOEocHYDfH+Bvz65k7aa9/PC8EQzrn974QSIiTaTE0c4FAgEef9n45LOdXDrhKI4b3ivaIYlIB6fE0c49984XvJ6/hXP+qx8Txuc2foCIyBFS4mjHlhRs4ek31/O1UdlccurgaIcjIp2EEkc7lf/ZTh59aQ2jBvbgynOGaVS4iLQaJY526PPNe/nrMyvo3yuVH100irhY/TOKSOvRJ047U1hUxp3zC0hLSeT6yXl0SQhn2XgRkeajxNGO7C6pYsYTBcT6Yrhhah7duiZEOyQR6YSUONqJ8soaZs4roLSymuun5JGVnhztkESkk1LiaAeqa/zcs3AZhUVlTLtoNAOyu0U7JBHpxJQ42ji/P8Ds51ex5ss9fP/c4Ywc2CPaIYlIJ6fE0YYFAgFmP7uCD9ZsZ8rpQzhhVHa0QxIRUeJoy15670uee3MdZ47P5ezjNCpcRNoGJY426p0Vhcx/fS0nj+3D1DOGaICfiLQZShxt0Ip1RTz84hqG909n+qXj8ClpiEjp2GeQAAAPoUlEQVQbosTRxqwvLObep1bQu2dXpk0aTXycln0VkbZFiaMN2ba7nFnzC0hJimf6lDySEjUqXETaHiWONmJv2T5mPJFPIAA3TM0jLSUx2iGJiByUEkcbUFFVw6z5Bewt28d1k8eQk9E12iGJiBySEkeU1dT6ue/pFWzcVsp/XzCKwb27RzskEZHDCqsS3Tl3GXATEA/MMrN7G5SPBWYD3YAlwLVmVhNSPg5YamaJwdc5wGNAJlAJXGNm+cGymcBZQAC41cz+eURX2Ib5AwEefnE1K9fv4nvnDCNvSM9ohyQi0qhGnzicc32AW4GTgLHA1c65EQ12exyYZmZDgRjgqpDjk4G7gdCpXG8DFphZHnAzcF9w3zOA44ExwBnAfcHjO6QnX1/Luyu3cdEpgzg5r3e0wxERCUs4VVUTgNfMbJeZlQELgEvqCp1z/YEkM1sa3PQIMDnk+DuAWQ3O+QPggeDPA4HdwZ9jgS54TzbJQFXYV9LOvPzBRha99yWnH92H807oH+1wRETCFk5VVW+gMOR1IXBcI+V9AZxzE4FkM1vgnKvfwcz8wfI1wADgguD2l51zVwObga7A/5pZeSQXlJGREsnuB8jMTG3ysZF485PN/OvVzzhhdA7XXXoMsb7DD/Brrbgipbgio7gio7gi05pxhZM4fHjtDXViAH9j5c65bLx2kQmHOrGZDQu2j7zsnBuG9yRTA2QDGcBi59x7IU8zjSoqKsXvDzS+YwOZmans2FES8XGRWv3FLmbOL2Bo3+5cefZQdhWVtom4IqW4IqO4IqO4InMkcfl8MRF/4Q6nqmoTkBPyOhvYEkb5eXgf/kucc3UN3/nOuVTn3DedcykAwUbxDcAgvCePx82s2sy2As8DJ0d0RW3Yl9tKuHvhcnqlJ/M/l4zRqHARaZfCSRyvAGc45zKDDdUXAy/VFZrZBqDSOXdicNN3gEVmNtvMBpvZWDMbG9x3rJmVAFcAVwMEG9qzgTVAAXBhcHtXvAbyD5vhOqNu554KZs4rICkxjulT8ujaJT7aIYmINEmjicPMNgO/AhYD+cBcM3vfOfeic258cLfLgZnBNosU4K5GTns9cLZzrgB4GLjUzErxem/FO+dWA+8Bj5nZ4qZcWFtSUr6PO+YVUF3j54YpefTo1iXaIYmINFlY4zjMbC4wt8G2c0N+LuDABvODnSMm5OctwNkH2acM72mkw6jaV8udC5ZRtLeSn31rLH0ym954LyLSFmjkeAuq9fu5/5kVrC8s5pqJIxmamxbtkEREjpgSRwsJBAI8+pKxbG0R3z7LcYzLjHZIIiLNQomjhTz95nreWlbI+V8bwOnj+kQ7HBGRZqPE0QIWf7yJ5975gpPH5HDhyQOjHY6ISLNS4mhmH9kOHn/5U/IGZ/DdbzitFS4iHY4SRzP6dOMe/vbsSgb17sa1F44i1qfbKyIdjz7ZmsnmHaXctWAZGd278JNLxpAYr1HhItIxKXE0g13FlcyYV0B8nI+fTskjNTmh8YNERNopJY4jVFZZzYx5BVTuq2H6lDx6piVFOyQRkRalxHEE9lXXcveCZWzbVc60i0bTr1fbnG5ZRKQ5KXE0kd8f4IHnVvHppr1cdf4Ihg/oEe2QRERahRJHEwQCAf7xn0/5+NMdXHrGURw3vFe0QxIRaTVKHE3w/LsbWPzJZs45vh9nHpsb7XBERFqVEkeE3izYwlNL1nHCyF5cfNrgaIcjItLqlDgiUPD5Th59yRg5sAffO3c4Po0KF5FOSIkjTGu37OX+p1eQ2yuFH104irhY3ToR6Zz06ReGwqIy7py/jLSURK6fnEdSYljrX4mIdEhKHI3YXVLFjCcKiImB6VPz6N5Vo8JFpHNT4jiM8soaZs0voLSimusn59ErPTnaIYmIRJ0SxyFU1/i596nlbNlZxo8vGsXAnG7RDklEpE1Q4jgIfyDAnBdWsXrDbr537jBGDcqIdkgiIm2GEkcDgUCAJ179nPdXb2fyaYP52qicaIckItKmKHE08O/3N/KfDzcyYXxfvnF8v2iHIyLS5nT6fqXvrtzKwjfWsqu4iq5JcZRW1HDssCy+dcZRWvZVROQgOnXieHflVh5dtIZ9NX4ASitqiImB0YMyNCpcROQQOnVV1cI31tYnjTqBADzz1rooRSQi0vZ16sRRVFwV0XYREenkiSOjW2JE20VEpJMnjkmnDiYh7sBbkBDnY9Kpmi5dRORQOnXj+AkjswHqe1X16JbIpFMH128XEZGv6tSJA7zkccLIbDIzU9mxoyTa4YiItHlhJQ7n3GXATUA8MMvM7m1QPhaYDXQDlgDXmllNSPk4YKmZJQZf5wCPAZlAJXCNmeU752KC7zMJSAb+YGaPHdkliohIc2q0jcM51we4FTgJGAtc7Zwb0WC3x4FpZjYUiAGuCjk+GbgbCJ2P/DZggZnlATcD9wW3Xw6cCRwPnAr8xTmX1oTrEhGRFhJO4/gE4DUz22VmZcAC4JK6QudcfyDJzJYGNz0CTA45/g5gVoNz/gB4IPjzQGB38OepwF/MbJ+ZbcVLVhXhX46IiLS0cKqqegOFIa8LgeMaKe8L4JybCCSb2QLnXP0OZuYPlq8BBgAXBIuGAMOdc9cDacCfzOyzCK5HRERaWDiJwwcEQl7HAP7Gyp1z2XjtFRMOdWIzGxZsH3nZOTcsGM8Y4GwgG3jbOfdJmMkjFiAjIyWMXQ8uMzO1yce2JMUVGcUVGcUVmQ4cV2y4O4ZTVbUJCJ1bPBvYEkb5eUAGsMQ5lw/gnMt3zqU6577pnEsBMLN8YAMwCNiK1/ZRbWYbgaXAuDCvRfOfi4g0XdifoTGBQOCwOwQbx9/Cq54qA94Brjaz90P2WYHXM+pt59wDwGdm9ucG5wmYWUzw53l4vaxmBBva/w0MB36ElyguA3oAHwNnmtmnYVxLInAsXlVZbRj7i4iI96SRA3wAhDXfUqNVVWa22Tn3K2AxXs+o2Wb2vnPuReA3ZvYhXm+oB51z3fA+7O9q5LTXAw87567A6457qZmVOudmArcDK4IX87swkwZ4F/xWmPuKiMh+ayPZudEnDhERkVCdeq4qERGJnBKHiIhERIlDREQiosQhIiIRUeIQEZGIKHGIiEhEOuV6HM65vwA9zezKBtv74c30mwUYcLmZlbaR2K4A/gRsC256wcx+1QrxLMa7H9XBTdeY2Xsh5ROAGUAS8ISZ3dTSMYUZ18N4k2SWBTf91syeaoW4zseb8bkr8LKZXdeg/LBLEEQxrpuB77N/wtEHGy6f0AIx/RCYFrJpIPCYmU0L2afV71eYcbX6/Qq+77eB/wu+XGRmP2tQ3iqfYZ0ucTjnzgCuAF44SPF9wH1m9i/n3K+BXwP/20ZiGw/cYGb/bMV4YoChQP+D/bE655KAh/CmwN8IvOCcO8fMFkUzrqDxwClmVniI8paIaxDwV7xlAbYBrx3kfjwO/NDMljrn5uAtQXB/G4hrPPAtM3u3JWMJZWaz8ZICzrmRwNPALQ12a/X7FWZcrX6/gktU3IX3u78Hby6/CWb2SshurfIZ1qmqqpxzPfDWFrntIGXxwCl408bDV6eHj1psQccCVzjnljvnHnfOpbdGWMH/v+ycK3DOTWtQfhze9DLrgx/gj9M69+ywcQX/wPoBDznnljnnfuuca43f9Yvwnro2mVk13jIBoU9BjS1BEJW4gsYDNwbv1z3OuS6tEFeo+4EbzWxn3YYo3q/DxhUUjfsVi/eZ3RVvUb14QpadaM3PsE6VOIC/Ab9i/+NlqJ5Accg32Prp4VvJ4WIDL57f480evBG4pxViSgdexfvgOQO41jl3Zkj5IafUj3Jc2cBreFUJ/wWcjLcGTEsbAsQ6554NTuz5Iw7894zW/TpsXMEJRz8Bfg4cjbekwa9bIa6695+AlyDmNyiK1v06bFzRul9mVhJ8nzV4k8t+gTd3YJ1W+wzrNFVVwXrLjWb2qnPuyoPs0nB6eDhw+vgWE0ZsmNlFIfvfToRzyzRF8DG8/lE8WFVwLvCf4KbGptyPSlxmtg4vqdSV3w18F3iwhUOLw/vGdxpQCjyLV/X4SLA8KversbiCdeDn1u3snLsDrwqyxdvQgq7BaydrKFr3q85B44rW/XLOjcH7MtQf2Iv3hP8zoG5C2Vb7DOtMTxxTgbOC37h+B0wMTqpYZzvQ3TlXNyd9DgdOHx+12Jxz3Z1z00P2jwFao0H1pGC7S+j7Voe8bmzK/ajE5Zwb7Zy7+FDlLWgr8IqZ7TCzCuApDlz0LCr3q7G4nHP9nHPfD9m/te4XzrkEvDayZw9SHK37ddi4oni/zgZeNbPtZlaFl/hPCylvtc+wTpM4zOxMMxtlZmOB3wDPmtn0kPJq4E28D3HwvqG2aCNvuLHhfUv8hXPu+ODraXh//C0tDfizc66Lcy4V71tq6Pu+Bzjn3JDgL+tltM49ayyuGGCWcy49WO97Na1zv54HznbOpQXvxznAR3WFZrYBqHTOnRjc9B1a534dNi68evLbnXMDgx0Pfkzr3C/wql4/DS5LfYAo3q/DxkX07lcBMME51zX4vufjTYUOtO5nWKdJHIfinJvtvCVuwav7vdo5twqvXrxVupYeSl1sZlYLTAHud86tBo4BftHS729mz+P18PoE74PmITN713kLcvU2s0rgSuBJYBVe3euCQ52vFeNaBvwReDsYV35r9EYLdge+HW96/1V4C5Q97Jx70Tk3Prjb5cBM5y2bnELjSxC0eFxmtgOvWuY5vC6cMcAdLR1X0CC8J4t60b5fjcUVrftlZi8D/8T7nV+G1zj+p2h8hmladRERiUinf+IQEZHIKHGIiEhElDhERCQiShwiIhIRJQ4REYmIEodIG+Cc+6Zz7nfRjkMkHEocIm3DsUCPaAchEg6N4xA5As5b5+ImIAEox5s76AO8AXfn4U0N8w7ewKwb8dZamRY89ha8iekeA57Bm/30gdZYZ0XkSOiJQ6SJnHNH4U2Df66ZjcOb2mQh3hQUxwB5wCgglf3TQHxFcGT3X/GmPlfSkDav08yOK9ICzsSbSO5V5+qWCMEPXIi3YlzdWglTof4JQ6TdU+IQabpYvNlK658mnHO5ePMpBUK29WL/lNcxIccntFKcIs1KVVUiTfcq3nT4wwCcc+fiTT63GLjMOZcYXHnwfuBSYAdwjHMuJjir73kh56rBm7ROpM1T4hBpIjNbhdeu8S/nXAHeCo0TgXvxZjD9CFiOtxLbXcA/8JLHZ3hTnb8RcrrX8KY+v7vVLkCkidSrSkREIqInDhERiYgSh4iIRESJQ0REIqLEISIiEVHiEBGRiChxiIhIRJQ4REQkIkocIiISkf8PpHfMad8KwUIAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "data_gamma.plot(x=\"ecut\", y=\"mode3\", style=\"-o\");"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's plot all the modes in different subplots with:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<Figure size 432x288 with 6 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "data_gamma.plot(x=\"ecut\", y=[k for k in data_gamma if k.startswith(\"mode\")], subplots=True, style=\"-o\");"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This convergence study at $\\Gamma$ thus reveals that our pseudos require \n",
    "an `ecut` >= 6 Ha to get reasonably converged phonon frequencies at $\\Gamma$.\n",
    "In what follows, we assume that also the modes at the other $q$-points present a similar\n",
    "convergence behaviour and we use `ecut` = 6 Ha to keep the computational cost low. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "For a quick introduction to Pandas, see:\n",
    "\n",
    "* [Pandas cookbook](https://github.com/jvns/pandas-cookbook)\n",
    "* [Pandas cookbook Chapter 1 Reading data from a csv file](http://nbviewer.jupyter.org/github/jvns/pandas-cookbook/blob/master/cookbook/Chapter%201%20-%20Reading%20from%20a%20CSV.ipynb)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Phonon band structure of AlAs\n",
    "[[back to top](#top)]\n",
    "\n",
    "Now we are finally ready for the calculation of the vibrational spectrum of $AlAs$.\n",
    "We already managed to run DFPT calculations at $\\Gamma$ with different values of `ecut` and the\n",
    "steps required to get a full band structure are not that different, provided that \n",
    "the following differences are taken into account:\n",
    "\n",
    "- we need the dynamical matrix $D(q)$ on a homogeneous mesh so that it is possible to calculate $D(R)$\n",
    "  in anaddb via Fourier transform and then phonon frequencies for arbitrary q-points via Fourier interpolation\n",
    "  \n",
    "- $AlAs$ is a polar semiconductor so we need to include the LO-TO splitting for $q \\rightarrow 0$ that, in turns,\n",
    "  requires the DFPT computation of the Born effective charges and of the dielectric constant.\n",
    "\n",
    "\n",
    "In AbiPy, these concepts are translated in an easy-to-use API in which you pass an initial `AbinitInput` object,\n",
    "you specify the q-mesh for phonons in terms of `ph_nqpt` and activate the computation of the \n",
    "Born effective charges with the boolean flag `with_becs`.\n",
    "\n",
    "Let's have a look at the code (as usual there are more comments than lines of code):"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
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       "\n",
       "<div class=\"highlight\"><pre><span></span><span class=\"k\">def</span> <span class=\"nf\">build_flow_alas_phonons</span><span class=\"p\">(</span><span class=\"n\">options</span><span class=\"p\">):</span>\n",
       "    <span class=\"sd\">&quot;&quot;&quot;</span>\n",
       "<span class=\"sd\">    Build and return a Flow to compute the dynamical matrix on a (2, 2, 2) qmesh</span>\n",
       "<span class=\"sd\">    as well as DDK and Born effective charges.</span>\n",
       "<span class=\"sd\">    The final DDB with all perturbations will be merged automatically and placed</span>\n",
       "<span class=\"sd\">    in the Flow `outdir` directory.</span>\n",
       "<span class=\"sd\">    &quot;&quot;&quot;</span>\n",
       "    <span class=\"n\">scf_input</span> <span class=\"o\">=</span> <span class=\"n\">make_scf_input</span><span class=\"p\">(</span><span class=\"n\">ecut</span><span class=\"o\">=</span><span class=\"mi\">6</span><span class=\"p\">,</span> <span class=\"n\">ngkpt</span><span class=\"o\">=</span><span class=\"p\">(</span><span class=\"mi\">4</span><span class=\"p\">,</span> <span class=\"mi\">4</span><span class=\"p\">,</span> <span class=\"mi\">4</span><span class=\"p\">))</span>\n",
       "    <span class=\"k\">return</span> <span class=\"n\">flowtk</span><span class=\"o\">.</span><span class=\"n\">PhononFlow</span><span class=\"o\">.</span><span class=\"n\">from_scf_input</span><span class=\"p\">(</span><span class=\"s2\">&quot;flow_alas_phonons&quot;</span><span class=\"p\">,</span> <span class=\"n\">scf_input</span><span class=\"p\">,</span>\n",
       "                                            <span class=\"n\">ph_ngqpt</span><span class=\"o\">=</span><span class=\"p\">(</span><span class=\"mi\">2</span><span class=\"p\">,</span> <span class=\"mi\">2</span><span class=\"p\">,</span> <span class=\"mi\">2</span><span class=\"p\">),</span> <span class=\"n\">with_becs</span><span class=\"o\">=</span><span class=\"bp\">True</span><span class=\"p\">)</span>\n",
       "</pre></div>\n",
       "</body>\n",
       "</html>\n"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from lesson_dfpt import build_flow_alas_phonons\n",
    "abilab.print_source(build_flow_alas_phonons)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can finally construct the flow with:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "flow_phbands = build_flow_alas_phonons(options=None)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "and visualize the connections with:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
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     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "flow_phbands.get_graphviz()\n",
    "#flow_phbands.plot_networkx();"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Note that there are a lot of things happening under the hood here.\n",
    "\n",
    "First of all, AbiPy generates `PhononTasks` only for the $q$-points in the \n",
    "irreducible wedge of the Brillouin zone corresponding to `ph_ngqpt`.\n",
    "Moreover, for a given $q$-point, only the irreducible atomic perturbations are explicitly computed\n",
    "since the other atomic perturbations can be reconstructed by symmetry.\n",
    "Fortunately you do not have to care about all these technical details as AbiPy and Abinit \n",
    "will automate the whole procedure.\n",
    "\n",
    "Remember that the $q$-point mesh cannot be chosen arbitrarily\n",
    "since all $q$ wavevectors should connect two $k$ points of the grid used for the electrons.\n",
    "\n",
    "It is also worth stressing that the computational cost of the DFPT run depends on the q-point \n",
    "since only those symmetries that preserve the q-point as well as the direction of the perturbation \n",
    "can be employed (calculations at $\\Gamma$ are therefore much faster than other q-points)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {
    "collapsed": false
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   "outputs": [
    {
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       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>rfphon</th>\n",
       "      <th>rfatpol</th>\n",
       "      <th>rfdir</th>\n",
       "      <th>qpt</th>\n",
       "      <th>kptopt</th>\n",
       "      <th>class</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>w0_t0</th>\n",
       "      <td>None</td>\n",
       "      <td>None</td>\n",
       "      <td>None</td>\n",
       "      <td>None</td>\n",
       "      <td>None</td>\n",
       "      <td>ScfTask</td>\n",
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       "      <th>w1_t0</th>\n",
       "      <td>None</td>\n",
       "      <td>None</td>\n",
       "      <td>(1, 0, 0)</td>\n",
       "      <td>(0, 0, 0)</td>\n",
       "      <td>2</td>\n",
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       "      <th>w1_t1</th>\n",
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       "      <td>[1, 0, 0]</td>\n",
       "      <td>(0, 0, 0)</td>\n",
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       "      <td>BecTask</td>\n",
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       "      <td>3</td>\n",
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      "text/plain": [
       "      rfphon rfatpol      rfdir              qpt kptopt       class\n",
       "w0_t0   None    None       None             None   None     ScfTask\n",
       "w1_t0   None    None  (1, 0, 0)        (0, 0, 0)      2     DdkTask\n",
       "w1_t1   None    None  (0, 1, 0)        (0, 0, 0)      2     DdkTask\n",
       "w1_t2   None    None  (0, 0, 1)        (0, 0, 0)      2     DdkTask\n",
       "w1_t3      1  [1, 1]  [1, 0, 0]        (0, 0, 0)      2     BecTask\n",
       "w1_t4      1  [2, 2]  [1, 0, 0]        (0, 0, 0)      2     BecTask\n",
       "w2_t0      1  [1, 1]  [1, 0, 0]  [0.5, 0.0, 0.0]      3  PhononTask\n",
       "w2_t1      1  [1, 1]  [0, 1, 0]  [0.5, 0.0, 0.0]      3  PhononTask\n",
       "w2_t2      1  [2, 2]  [1, 0, 0]  [0.5, 0.0, 0.0]      3  PhononTask\n",
       "w2_t3      1  [2, 2]  [0, 1, 0]  [0.5, 0.0, 0.0]      3  PhononTask\n",
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       "w3_t1      1  [2, 2]  [1, 0, 0]  [0.5, 0.5, 0.0]      3  PhononTask"
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "flow_phbands.get_vars_dataframe(\"rfphon\", \"rfatpol\", \"rfdir\", \"qpt\", \"kptopt\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now we can generate the directories and the input files of the `Flow`.\n",
    "Change lesson_dfpt.py so that the build_flow_alas_phonons function is called in main\n",
    "instead of build_flow_alas_ecut_conv. \n",
    "Run the script to generate the directory with the flow.\n",
    "Finally, use \n",
    "\n",
    "    abirun.py flow_alas_phonons scheduler\n",
    "    \n",
    "to launch the entire calculation."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Post-processing the results\n",
    "[[back to top](#top)]\n",
    "\n",
    "Our flow is completed and we have the final DDB file with all the $q$-points and all the independent atomic perturbations. \n",
    "Let's open this DDB file with:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "================================= File Info =================================\n",
      "Name: out_DDB\n",
      "Directory: /Users/gmatteo/git_repos/abitutorials/abitutorials/dfpt/flow_alas_phonons/outdata\n",
      "Size: 28.11 kb\n",
      "Access Time: Sun Aug 12 00:43:48 2018\n",
      "Modification Time: Thu Oct 12 22:34:40 2017\n",
      "Change Time: Thu Oct 12 22:34:40 2017\n",
      "\n",
      "================================= Structure =================================\n",
      "Full Formula (Al1 As1)\n",
      "Reduced Formula: AlAs\n",
      "abc   :   3.970101   3.970101   3.970101\n",
      "angles:  60.000000  60.000000  60.000000\n",
      "Sites (2)\n",
      "  #  SP       a     b     c\n",
      "---  ----  ----  ----  ----\n",
      "  0  Al    0     0     0\n",
      "  1  As    0.25  0.25  0.25\n",
      "\n",
      "Abinit Spacegroup: spgid: 0, num_spatial_symmetries: 24, has_timerev: True, symmorphic: False\n",
      "\n",
      "================================== DDB Info ==================================\n",
      "\n",
      "Number of q-points in DDB: 3\n",
      "guessed_ngqpt: [2 2 2] (guess for the q-mesh divisions made by AbiPy)\n",
      "Has total energy: False, Has forces: False\n",
      "Has stress tensor: False\n",
      "\n",
      "Has (at least one) atomic pertubation: True\n",
      "Has (at least one diagonal) electric-field perturbation: True\n",
      "Has (at least one) Born effective charge: True\n",
      "Has (all) strain terms: False\n",
      "Has (all) internal strain terms: False\n",
      "Has (all) piezoelectric terms: False\n"
     ]
    }
   ],
   "source": [
    "ddb = abilab.abiopen(\"flow_alas_phonons/outdata/out_DDB\")\n",
    "print(ddb)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The `DdbFile` object provides an easy-to-use interface that invokes `anaddb` to post-process\n",
    "the data stored in the DDB file.\n",
    "\n",
    "`anacompare_phdos`, for example, computes the phonon DOS with different $q$-meshes.\n",
    "Each mesh is defined by a single integer, `nqsmall`, that gives the number of \n",
    "divisions used to sample the smallest reciprocal lattice vector. \n",
    "The number of divisions along the other directions are chosen so that proportions are preserved:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "c = ddb.anacompare_phdos(nqsmalls=[8, 10, 12, 14, 16])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "c.plotter.combiplot();"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "A 16x16x16 $q$-mesh with the tethraedron method gives a well converged phonon DOS."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "To function `anaget_phbst_and_phdos_files` allows one to compute the phonon band structure on an automatically defined $q$-path as well as the the phonon DOS:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "phbst_file, phdos_file = ddb.anaget_phbst_and_phdos_files(ndivsm=10, nqsmall=16, lo_to_splitting=False)\n",
    "\n",
    "# Extract the phonon bands and the phonon DOS from phbst_file and phdos_file\n",
    "phbands = phbst_file.phbands \n",
    "phdos = phdos_file.phdos"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's plot the bands with matplotlib:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "phbands.plot();"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "and the high-symmetry q-path:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "phbands.qpoints.plot();"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Do you see the two strange dips for the highest phonon band, at the $\\Gamma$ point?\n",
    "They are due to the lack of LO-TO splitting for the ANADDB treatment of the first list of vector. \n",
    "See also the discussion in the [second DFPT lesson](https://docs.abinit.org/tutorial/rf2/index.html)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "For years, Abinit users had to patch manually the output frequencies to include the LO-TO splitting.\n",
    "These days are finally gone and we can plot the LO-TO splitting with AbiPy by just setting\n",
    "lo_to_splitting=True`:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "phbst_file, phdos_file = ddb.anaget_phbst_and_phdos_files(ndivsm=10, nqsmall=16, lo_to_splitting=True)\n",
    "\n",
    "# Extract the phonon bands and the phonon DOS from phbst_file and phdos_file\n",
    "phbands = phbst_file.phbands \n",
    "phdos = phdos_file.phdos"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "#phbst_file.phbands.qpoints.plot(); "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The band structure plot now correctly shows the non-analytical behaviour around $\\Gamma$:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "phbands.plot();"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<div class=\"alert alert-warning\">\n",
    "`lo_to_splitting=True` works only when the DDB contains the Born effective charges and the dielectric constant,\n",
    "that must be computed in the Abinit run.\n",
    "</div>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "To plot bands and DOS on the same figure:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "phbands.plot_with_phdos(phdos);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The `PhdosFile` contains the phonon frequencies, the displacement vectors\n",
    "as well as the decomposition of the total DOS in terms of the contributions due to \n",
    "the different types of atom in the unit cell.\n",
    "This means that one can plot the type-projected phonon DOS with:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "phdos_file.plot_pjdos_type(title=\"AlAs type-projected phonon DOS\");"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "and it is even possible to plot fatbands and type-projected DOSes on the same figure with:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 4 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "phbands.plot_fatbands(phdos_file=phdos_file);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The highest frequency modes have a strong Al-character while the low frequency modes originate from As. \n",
    "This behaviour is somehow expected. Could you explain it in terms of a simple physical model?   "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Macroscopic dielectric tensor and Born effective charges\n",
    "[[back to top](#top)]\n",
    "\n",
    "Our calculations includes the response of the system to an external electric field.\n",
    "The code below extracts the macroscopic dielectric tensor (`emacro`)\n",
    "and the Born effective charges (`becs`) from the DDB file:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "emacro, becs = ddb.anaget_emacro_and_becs()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "DielectricTensor([[ 1.03961652e+01 -0.00000000e+00 -0.00000000e+00]\n",
       " [-0.00000000e+00  1.03961652e+01  1.19611765e-15]\n",
       " [-0.00000000e+00  1.19611765e-15  1.03961652e+01]])"
      ]
     },
     "execution_count": 40,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "emacro"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>element</th>\n",
       "      <th>frac_coords</th>\n",
       "      <th>xx</th>\n",
       "      <th>yy</th>\n",
       "      <th>zz</th>\n",
       "      <th>yz</th>\n",
       "      <th>xz</th>\n",
       "      <th>xy</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>Al</td>\n",
       "      <td>[0.0, 0.0, 0.0]</td>\n",
       "      <td>2.168053</td>\n",
       "      <td>2.168053</td>\n",
       "      <td>2.168053</td>\n",
       "      <td>-2.087488e-19</td>\n",
       "      <td>-2.087488e-19</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>As</td>\n",
       "      <td>[0.25, 0.25, 0.25]</td>\n",
       "      <td>-2.168053</td>\n",
       "      <td>-2.168053</td>\n",
       "      <td>-2.168053</td>\n",
       "      <td>2.087488e-19</td>\n",
       "      <td>2.087488e-19</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "Born effective charges in Cartesian coordinates (Voigt notation)\n",
       "  element         frac_coords        xx        yy        zz            yz            xz   xy\n",
       "0      Al     [0.0, 0.0, 0.0]  2.168053  2.168053  2.168053 -2.087488e-19 -2.087488e-19  0.0\n",
       "1      As  [0.25, 0.25, 0.25] -2.168053 -2.168053 -2.168053  2.087488e-19  2.087488e-19  0.0\n",
       "\n",
       "Born effective charge neutrality sum-rule with chneut: 1\n",
       "\n",
       "[[0.00000000e+00 0.00000000e+00 0.00000000e+00]\n",
       " [0.00000000e+00 0.00000000e+00 0.00000000e+00]\n",
       " [2.40741243e-35 2.40741243e-35 0.00000000e+00]]"
      ]
     },
     "execution_count": 41,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "becs"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "As explained in the references, the Born effective charges must fulfill \n",
    "the charge neutrality sum-rule.\n",
    "This rule is usually broken due to the discretization introduced by the FFT mesh, and `anaddb` will enforce it if `chneut` is set to 1 (default behaviour). Let's check it out!"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Born effective charges in Cartesian coordinates (Voigt notation)\n",
      "  element         frac_coords        xx        yy        zz            yz            xz   xy\n",
      "0      Al     [0.0, 0.0, 0.0]  2.168053  2.168053  2.168053 -2.087488e-19 -2.087488e-19  0.0\n",
      "1      As  [0.25, 0.25, 0.25] -2.168053 -2.168053 -2.168053  2.087488e-19  2.087488e-19  0.0\n",
      "\n",
      "Born effective charge neutrality sum-rule with chneut: 1\n",
      "\n",
      "[[0.00000000e+00 0.00000000e+00 0.00000000e+00]\n",
      " [0.00000000e+00 0.00000000e+00 0.00000000e+00]\n",
      " [2.40741243e-35 2.40741243e-35 0.00000000e+00]]\n"
     ]
    }
   ],
   "source": [
    "print(becs)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's repeat the same calculation but without enforcing the sum-rule:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Born effective charges in Cartesian coordinates (Voigt notation)\n",
      "  element         frac_coords        xx        yy        zz            yz            xz   xy\n",
      "0      Al     [0.0, 0.0, 0.0]  2.127295  2.127295  2.127295  8.199282e-20  8.199282e-20  0.0\n",
      "1      As  [0.25, 0.25, 0.25] -2.208811 -2.208811 -2.208811  4.994904e-19  4.994904e-19  0.0\n",
      "\n",
      "Born effective charge neutrality sum-rule with chneut: 0\n",
      "\n",
      "[[-8.15163891e-02  0.00000000e+00  0.00000000e+00]\n",
      " [ 0.00000000e+00 -8.15163891e-02  0.00000000e+00]\n",
      " [ 5.81483171e-19  5.81483171e-19 -8.15163891e-02]]\n"
     ]
    }
   ],
   "source": [
    "emacro, becs_chneut0 = ddb.anaget_emacro_and_becs(chneut=0)\n",
    "print(becs_chneut0)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Thermodynamic properties within the harmonic approximation\n",
    "[[back to top](#top)]\n",
    "\n",
    "The thermodynamic properties of an ensemble of non-interacting phonons can be \n",
    "expresses in terms of integrals of the DOS.\n",
    "\n",
    "\\begin{equation} %\\label{eq:helmholtz}\n",
    "\\Delta F = 3nNk_BT\\int_{0}^{\\omega_L}\\text{ln}\\left(2\\text{sinh}\\frac{\\hbar\\omega}{2k_BT}\\right)g(\\omega)d\\omega\n",
    "\\end{equation}\n",
    "\n",
    "\\begin{equation} %\\label{eq:free_en}\n",
    "\\Delta E = 3nN\\frac{\\hbar}{2}\\int_{0}^{\\omega_L}\\omega\\text{coth}\\left(\\frac{\\hbar\\omega}{2k_BT}\\right)g(\\omega)d\\omega\n",
    "\\end{equation}\n",
    "\n",
    "\\begin{equation} %\\label{eq:c_v}\n",
    "C_v = 3nNk_B\\int_{0}^{\\omega_L}\\left(\\frac{\\hbar\\omega}{2k_BT}\\right)^2\\text{csch}^2\\left(\\frac{\\hbar\\omega}{2k_BT}\\right)g(\\omega)d\\omega\n",
    "\\end{equation}\n",
    "\n",
    "\n",
    "\\begin{equation} %\\label{eq:entropy}\n",
    "S = 3nNk_B\\int_{0}^{\\omega_L}\\left(\\frac{\\hbar\\omega}{2k_BT}\\text{coth}\\left(\\frac{\\hbar\\omega}{2k_BT}\\right) - \\text{ln}\\left(2\\text{sinh}\\frac{\\hbar\\omega}{2k_BT}\\right)\\right)g(\\omega)d\\omega,\n",
    "\\end{equation}\n",
    "\n",
    "where $k_B$ is the Boltzmann constant.\n",
    "\n",
    "This should represent a reasonable approximation especially in the low temperature \n",
    "regime in which anharmonic effects can be neglected.   \n",
    "\n",
    "Let's plot the vibrational contributions thermodynamic properties as function of $T$: "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 4 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "phdos.plot_harmonic_thermo();"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Exercises\n",
    "[[back to top](#top)]\n",
    "\n",
    "* Our first phonon band structure has been computed with a (4, 4, 4) $k$-mesh \n",
    "  for the electrons and a (2, 2, 2) $q$-mesh for phonons. \n",
    "  You may try to increase the density of $k$-points/$q$-points\n",
    "  to see if this change affects the final results.\n",
    "        \n",
    "* Why do you get an error from AbiPy if you try `ngkpt` = (4, 4, 4,) and `ngqpt` = (3, 3, 3)?"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Back to the main [Index](../index.ipynb)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
 ],
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